Total Energy of An electron:

In n^th orbit of an atom:

It includes the e^- kinetic energy and the electrostatic potential energy of the 2 charges.

Kinetic Energy of an e^- in n^th orbit

Is K.E. = (1/2) mv²                                           —(7)

From equation number (2) and (7)

K.E. = (1/2) mv² = (1/2) (K Ze²/r)                                —(8)

Now potential energy of the electron is n^th orbit is

P.E. = k q₁q₂/r = -k (Ze) e/r = -k Ze²/r

P.E. = -k Ze²/r

Total energy of the electron in the n^th orbit

E_n = T.E. = P.E. + K.E.

--> T.E. = (K Ze²/2r) – (K Ze²/r)

T.E. = -KZe²/2r

Now  from equation                       —(6)

E_n = T.E. = (-K Ze²/2) x (4π²m K Ze²/n²h²)

E_n = T.E. = -2π²m K² Z²/n² h²                         —(10)

The negative value of the total energy indicates that the e^- is bound to the nucleus by means of electrostatic interaction and same work is required to be done to pule it away from the nucleus.

# Expression for the wave number of radiations emitted by an e^-, when it jump from outer orbit to lower orbit.